Since rRNA comprises about 95% to about 98% of the RNA in a cell, its presence can complicate various types of analyses of other RNA molecules of interest in a sample (e.g., gene expression analyses by arrays or microarrays, next-generation sequencing of tagged cDNA molecules made from one or more types of RNA molecules in samples (e.g., using the massively parallel digital sequencing methods referred to as “RNA-seq”), etc.). The problems caused by rRNA are especially difficult for analyses of RNA molecules of interest that are fragmented. For example, a considerable and continuing problem in the art is to find better methods for removing degraded rRNA from formalin-fixed paraffin-embedded (FFPE) tissue sections. If better methods were available to remove degraded rRNA from samples (e.g., FFPE-derived samples), it is believed that the enormous quantities of clinical specimens, for which medical outcomes of various diseases and various treatments are recorded in the medical records, would provide extremely valuable information related to identifying RNAs involved in the cause, maintenance, response, diagnosis, or prognosis of many diseases, such as cancer. Still further, better methods for removing rRNA, including degraded rRNA, from non-rRNA RNA molecules of interest would greatly improve the applicability and success of methods that comprise deliberately degrading the RNA as part of the particular method (such as the method of Ingolia et al., Science 324: 218-23, 2009, herein incorporated by reference).